Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System
This study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numeri...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2023/6916596 |
| _version_ | 1797392236510445568 |
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| author | Israa Th. Younis Ekhlass S. Al-Rawi |
| author_facet | Israa Th. Younis Ekhlass S. Al-Rawi |
| author_sort | Israa Th. Younis |
| collection | DOAJ |
| description | This study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order. |
| first_indexed | 2024-03-08T23:44:20Z |
| format | Article |
| id | doaj.art-09b2b36c0b6646679c4b73348be00b2f |
| institution | Directory Open Access Journal |
| issn | 1687-0425 |
| language | English |
| last_indexed | 2024-03-08T23:44:20Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj.art-09b2b36c0b6646679c4b73348be00b2f2023-12-14T00:00:22ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences1687-04252023-01-01202310.1155/2023/6916596Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson SystemIsraa Th. Younis0Ekhlass S. Al-Rawi1Department of MathematicsDepartment of MathematicsThis study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order.http://dx.doi.org/10.1155/2023/6916596 |
| spellingShingle | Israa Th. Younis Ekhlass S. Al-Rawi Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System International Journal of Mathematics and Mathematical Sciences |
| title | Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System |
| title_full | Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System |
| title_fullStr | Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System |
| title_full_unstemmed | Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System |
| title_short | Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System |
| title_sort | improved finite difference technique via adomian polynomial to solve the coupled drinfeld s sokolov wilson system |
| url | http://dx.doi.org/10.1155/2023/6916596 |
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